Beam machining is characterized by a machining action utilizing an extremely high energy density and is increasingly being used for machining hard materials. A brittle material such as a ceramic which is difficult to machine with other processes can also be machined advantageously by beam machining thanks to the fact that the high energy density machining ability allows a high machining rate and hence machining feed. Thus, while the problem of cracking has been found to be alleviated, this problem has not completely been solved by the prior beam machining technique. Furthermore, regardless of kinds of materials, beam-machining efficiency could seldom be optimized in the prior technique.